How Does the First Molar Root Location Affect the Critical Stress Pattern in the Periodontium? A Finite Element Analysis

Statement of the Problem: The first molar root location plays a pivotal role in neutralization of forces applied to the teeth to prevent injury. Purpose: This study aimed to assess the effect of maxillary and mandibular first molar root location on biomechanical behavior of the periodontium under vertical and oblique loadings. Materials and Method: In this three-dimensional (3D) finite element analysis (FEA), the maxillary and mandibular first molars and their periodontium were modeled. The Young’s modulus and the Poisson’s ratio for the enamel, dentin, dental pulp, periodontal ligament (PDL), and cortical and cancellous bones were adopted from previous studies. The changes in maximum von Misses stress (MVMS) values of each component were analyzed. Results: The MVMS values were the highest in the enamel followed by dentin, cortical bone, cancellous bone, and PDL. The maxillary and mandibular first molars with different root locations and their periodontium showed different biomechanical behaviors under the applied loads. Conclusion: An interesting finding was that the stress concentration point in the path of load degeneration changed from the cervical third in dentin to the apical third in the cancellous bone, which can greatly help in detection of susceptible areas over time.


Introduction
The periodontium plays a fundamental role in transfer of masticatory forces from the tooth to the alveolar bone, and force degradation [1]. From the clinical point of view, excessive occlusal forces can damage the periodontal tissue, temporomandibular joint, masticatory muscles, and pulp tissue [2]. However, from the biological point of view, animal studies have indicated that excessive loading is associated with the formation of pressure and tension sites in bone, depending on the magnitude and direction of the applied forces. The pressure sites are characterized by bone resorption, while the tension sites are characterized by bone remodeling [3][4][5]. The occurrence of the bone remodeling process depends on the maximum load and number of fixed daily cycles of load application [6][7][8]. It appears that the pattern and location of maximum stress concentration may differ depending on the root location of molar teeth. Therefore, pattern of stress distribution in teeth with different morphologies and biomechanical behavior of the components (which are not homogenous) should be studied in physiological occlusion and under maximum mastication force (MMF). Evidence shows that the teeth are more resistant to vertical loads. Thus, occlusal stress is considered as the main cause of dental injury [4,[9][10][11][12][13][14].
It can traumatize the tooth at the stress concentration points and even lead to tooth fracture over time [15][16].
Detection of stress concentration points in the tooth structure and periodontium is not easy. A precise biomechanical model is required to analyze the causes of tooth fracture through a finite element analysis (FEA).
Borčić et al. [30]  MPa) and also in the central fossa of both models (about +28 MPa) in the cusp to fossa and cusp to marginal ridge occlusion. They only evaluated the stress distribution pattern in the tooth structure, and maximum stress concentration was noted in dentin and enamel in the cervical region [30]. It seems the location of roots can also affect these maximum stress points on the periodontium. Therefore, the pattern of stress distribution and degradation should be studied to find the actual points of stress accumulation and susceptible areas at which, the stress level might exceed the tolerance threshold of the tissue. Since first molars are the largest posterior teeth and have the most complex morphology [35], they play a fundamental role in distribution of masticatory forces [32][33][34][35].

Loading process
The loading process was adopted from the studies by Jiang et al. [37], Yoon et al. [45], and Yuan et al. [46], for vertical and lateral loadings (in order to be able to compare the results). According to Jiang et al. [37], vertical load was applied to 5 points in the occlusal surface of the maxillary first molar, and lateral forces were also applied to the lingual slope of the lingual cusp.
Moreover, according to Yoon et al. [45], vertical load was applied to 5 points in the occlusal surface of the mandibular first molar that were in contact with the opposing tooth during mastication. According to Yuan et al. [46], lateral forces were applied to two points in the lingual slope of the buccal cusps at 45-degree angle relative to the longitudinal axis of the tooth. It should be noted that the magnitude of vertical and lateral loads was distributed among the loaded points. Therefore, three loading conditions were considered for FEA as follows:

Loading condition 1
Axial load in an amount of 250 N [47] was applied to 5 points in the occlusal surface to simulate normal application of masticatory forces in the clinical setting. These points were the central fossa, mesial and distal marginal ridges, and the center of the buccal cusps in the mandibular first molar [45], and the central fossa, mesial and distal marginal ridges, and the center of the palatal cusps in the maxillary first molar [37].

Loading condition 2
Oblique load in an amount of 100 N [11] with 45degree angle was applied to simulate lateral forces applied during mastication in the clinical setting. The loading points were the internal slope of the buccal cusps of the mandibular first molar [46] and the internal slope of the palatal cusps of the maxillary first molar.

Loading condition 3
Axial load in an amount of 800N [45,48] was applied to the same points mentioned above in the maxillary and

Results
The MVMS values in the six models were analyzed in different tissues to find the effect of root location on susceptible high-stress points in the maxillary (with mesial, distal, and palatal root locations) and mandibular (with mesial and distal root locations) first molars and their periodontium. Figure 3 shows the results of loading of the occlusal surface, which is the first surface that receives the applied forces.   After passing through the tooth structure, stress reaches the PDL. Figure 5 shows the stress distribution in the PDL. As shown, the magnitude of stress in the PDL was lower than the corresponding value in dental   Also, Guler et al. [26] reported that the stress value applied to the occlusal surface of a maxillary first molar with an intact occlusal surface and a class V restoration was 70-90 MPa under masticatory forces (Figure 8a).
Similarly, in the mandible, comparisons with some other studies indicated 80 MPa maximum stress accumulation in the occlusal surface of restored teeth [49][50] ( Figure 8b).

Discussion
Evidence shows that the periodontium transfers the ma- on the tooth support mechanism, which is impaired when the periodontium is damaged [51]. Thus, periodontal adaptation is affected by the magnitude, direction, duration, and frequency of load application. When the applied occlusal forces exceed the maximum adaptation capacity of a tooth, tissue injury or trauma from occlusion may occur [52].
Animal studies have revealed the histological events responsible for this adaptation, which include bone for-mation at the tension sites and bone resorption at the pressure sites in the periodontium [53][54][55][56][57].Thus, detection of high-stress and tension points and their generalization to the clinical setting seem imperative. In the present study, both occlusal tables received a vertical occlusal force with the same magnitude at 5 points to simulate physiological and MMF loading conditions [37,45,[47][48] and at 2 points for simulation of lateral forces applied to the teeth in function according to previous studies [37,58].
The results of the present study indicated MVMS concentration in the occlusal enamel and cervical dentin (Figures 3-4). These areas are in conformity with those reported by the previous studies in different teeth [42][43][59][60]. The points of MVMS concentration in the enamel are depicted in graphs in Figures 3-8. For a more accurate analysis, the results were compared with the findings of Jiang et al. [37] and Guler et al. [26]. Regarding the MVMS values, the findings of Jiang et al. [37] and Guler et al. [26] were almost consistent with the present results. However, they did not make a comparison between the maxillary and mandibular molar teeth.
High stress concentration in the enamel, as reported in many studies, is due to the hardness and high modulus of elasticity of the enamel as well as its higher resistance against the applied forces. Thus, enamel tolerates high levels of stress and significantly decreases the magnitude of stress, which is higher in three-rooted first molars under vertical loading compared with two-rooted first molars and vice versa under oblique loads ( Figure   3).
Considering the lower hardness of dentin than enamel, the magnitude of stress decreased in dentin ( Figure   4a). Stress concentration in the maxillary first molar dentin was mainly in the palatal and mesiobuccal roots under standard loading. Under parafunctional forces, the concentration of stress was in the mesiobuccal root, while under oblique loading, stress concentrated in the cervical third of the palatal root. These results were in line with the previous findings [61]. In the mandibular first molar, however, the masticatory loads were mainly distributed through the buccal surface of the mesial root.
Under oblique loading, stress was transferred from the buccal surface of the tooth crown and lingual surface of the distal root [62][63]. This finding has been confirmed by the authors who assessed stress distribution in dentin of endodontically-treated teeth using FEA. They added that considering the stress accumulation points, endodontic posts should be preferably placed in the distal root [36,45]. These changes are due to the fact that the first molar mesial root has a wider buccolingual than mesiodistal dimension, and has an ovoid shape [64].
Thus, it receives higher stress levels in this dimension, which can lead to vertical fracture in this dimension. On the other hand, considering the morphology and higher concavity of the mesial root than the distal root, and the difference in the load application axis and stress accumulation points between the two roots, higher torque is generated in the mesial root [65][66]. It should be noted that since the root dentin is thin at the apex, cracks often initiate from the apical region in such fractures [67][68].
However, under oblique loading, the maximum stress is accumulated in the cervical third of the distal root, which is probably due to the proximity of dentin to the alveolar bone crest. Bone crest serves as a lever and generes torque, which results in further damage under masticatory loads, causing mainly horizontal fractures [63,69].
In general, the results revealed that the stress concentration point in load transfer from the tooth to the attachment apparatus changes from the cervical dentin towards the middle third in the lamina dura, and then to the apical third in the cancellous bone in two-rooted and three-rooted first molars. In the PDL, stress concentration occurs at the interface of the cervical third and middle third (Figures 5-7). Similarly, Poiate et al. [69] reported stress concentration in the same points in the PDL of a maxillary central incisor. In addition, some researchers reported that the point of maximum stress concentration changed from the coronal third in dentin of a sound tooth to middle or apical third in an endodontically treated tooth [45,[70][71][72]. These areas are the sites of maximum collagen fiber degradation and alveolar bone loss. It appears that the oblique fibers in the PDL, mainly located in the middle third of the root, are responsible for this process [71]. Thus, loads are trans-